Randomized controlled trials are currently the gold standard within evidence-based medicine. Usually they are monitored for early signs of effectiveness or harm. However, evidence from trials stopped early is often charged with bias toward implausibly large effects. To our mind, this skeptical attitude is unfounded and caused by the failure to perform appropriate conditioning in the statistical analysis of the evidence. We contend that conditional hypothesis tests give a superior appreciation of the obtained evidence and significantly improve the practice of sequential medical trials, while staying firmly rooted in frequentist methodology